Sure, it's a private business. They can't throw you in jail or fine you for it though, unless you refuse to leave when asked, then it's trespassing. A school, except a private school, is a public place, and is at least quasi governmental as well. They are restricted by the constitution, whereas the mall management is not.
I clearly used a crappy example, so try replacing "mall" with "White House", or "Congress", or "post office", or the incredibly generic "any federal installation".